Having a little trouble deriving a result in a book.(adsbygoogle = window.adsbygoogle || []).push({});

If I have an operator of the form [tex]e^{\alpha A \otimes I_n}[/tex]

Where alpha is a complex constant, A a square hermitian matrix and I the identity matrix.

Now if I want to operator that on a tensor product, say for instance [tex]c_{n,1} |1 \rangle \otimes |n \rangle[/tex] then how would I do that?

I firstly used the identity [tex]e^{\alpha A \otimes I_n} = e^{\alpha A \otimes I_n} [/tex] to obtain:

[tex]e^{\alpha A \otimes I_n} {} | c_{n,1} |1 \rangle \otimes |n \rangle \rangle = e^{\alpha A} \otimes I_n {} |c_{n,1} {}|1\rangle \otimes |n \rangle \rangle = c_{n,1} e^{\alpha A}{}|1\rangle \otimes |n \rangle [/tex]

but my book gets [tex]c_{n,1} e^{\alpha}|1 \rangle \otimes |n \rangle [/tex] with no further explanation. By the way the form of the matrix [tex] A = \begin{pmatrix} 1 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & -1 \end{pmatrix} [/tex] if it helps to know it.

Also I am aware you can represent [tex]e^{\alpha A}[/tex] in the form of an infinite series but I don't see how that helps here. In fact I tried it and I didn't know where I should cut the series off at, and it gave me coefficients of alpha rather than e^alpha. Oh and the n's are being summed over, not sure if that makes any difference.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Unitary Operator on a Tensor Product

Loading...

Similar Threads for Unitary Operator Tensor | Date |
---|---|

B Question about Unitary Operators and symmetry | Feb 9, 2018 |

A Forming a unitary operator from measurement operators | Jun 27, 2017 |

Prove the time evolution operator is unitary | Dec 26, 2015 |

Unitary and linear operator in quantum mechanics | Dec 6, 2015 |

What is the suitable unitary operator for a rotating frame? | Nov 8, 2014 |

**Physics Forums - The Fusion of Science and Community**